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I t can solve many calculus problems at a click of a button. In order to make full use of Maple's power you have to learn the way of telling M aple what you want it to do; that is, you have to learn the correct Ma ple" }{TEXT 294 1 " " }{TEXT 269 6 "syntax" }{TEXT 293 2 ". " }{TEXT -1 43 "You also have to learn how to handle Maple " }{TEXT 257 10 "wor ksheets" }{TEXT 295 2 ". " }{TEXT -1 137 "Below is a short introductio n to using Maple and its basic commands. We shall introduce more advan ced commands in subsequent worksheets. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT -1 16 "Maple Worksheets" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 261 1 " " }{TEXT -1 161 "A works heet, like this one, consists of text and Maple command lines. You tog gle between the text mode and the command line mode by pressing the bu ttons marked \"" }{TEXT 258 1 "T" }{TEXT -1 16 "\" for text and \"" } {TEXT 259 2 "[>" }{TEXT -1 89 "\" for the command line. The buttons ar e located on the toolbar above. (The third button \"" }{XPPEDIT 296 0 "Sigma;" "6#%&SigmaG" }{TEXT -1 214 " \" allows you to enter mathemati cal equations while in the text mode. You will not have to use this bu tton much.) You enter text in the text mode. You enter Maple commands \+ in the command mode following the prompt \"" }{TEXT 297 1 ">" }{TEXT -1 438 "\". Commands that you type usually appear in red. Each command has to end with a semicolon. (Ocassionally, if you don't want Maple t o print out the output you end your command with a colon.) After you a re finished typing a command press \"Enter\" and Maple returns an outp ut. Outputs are usually displayed in blue. You save worksheets and ope n new worksheets by clicking on the appropriate icons on the toolbar, \+ as in any other application. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 124 "We shall switch now to a command line mo de and ask Maple to perform some simple calculations. Let's tell Maple to calculate " }{XPPEDIT 18 0 "2*(359+23)-(5+21)/(2+11)+25^9/32456789 999;" "6#,(*&\"\"#\"\"\",&\"$f$F&\"#BF&F&F&*&,&\"\"&F&\"#@F&F&,&F%F&\" #6F&!\"\"F0*&\"#D\"\"*\",****ycC$F0F&" }{TEXT -1 88 " . We type our co mmand at the command prompt, press \"Enter\" and Maple returns an answ er." }}{PARA 0 "" 0 "" {TEXT -1 4 " " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "2*(359+23)-(5+21)/(2+11)+25^9/32456789999;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6##\"/j[CrnaG\",****ycC$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 136 "As y ou see, the rules of entering arithmetical operations are similar to t hose on your calculator. Multiplication is always denoted by \"" } {TEXT 298 1 "*" }{TEXT -1 16 "\", division by \"" }{TEXT 299 1 "/" } {TEXT -1 22 "\", exponentiation by \"" }{TEXT 300 1 "^" }{TEXT -1 246 "\", addition and subtraction in the obvious way. The proper use of pa retheses is, of course, crucial to correct syntax. As in the above exa mple, whenever possible Maple will return an exact answer. If you want a decimal form, or in other words, a " }{TEXT 302 28 "floating point \+ approximation" }{TEXT -1 46 " of your answer, you have to use the comm and \"" }{TEXT 301 5 "evalf" }{TEXT -1 92 "\". (The\"f\"at the end of \+ the command stands for the \"floating point\", \"eval\" for \"evaluate \".)" }}{PARA 0 "" 0 "" {TEXT -1 2 " " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+KcJ&o )!\"(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 12 "The symbol \"" }{TEXT 303 1 "%" }{TEXT -1 41 " \" in Release 5 of Maple denotes the last " }{TEXT 265 8 "executed" } {TEXT 304 1 " " }{TEXT -1 77 "output; that is the output of the comman d on which you clicked last. (It was " }{TEXT 305 1 "\"" }{TEXT -1 13 " instead of " }{TEXT 306 1 "%" }{TEXT -1 35 " in earlier releases.) \+ The symbol \"" }{TEXT 307 1 "%" }{TEXT -1 260 "\" easily leads to conf usion and you will be better off using it always on the same command l ine as the command to which it refers. You can enter several commands \+ on one line, end each with a semicolon, and then press \"Enter\" to ex ecute all of them. For example" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "(2*7+23)/(17-2); evalf(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6##\"#P\"#:" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+nmmmC!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 90 "Maple gave the exact ver sion of the answer, followed by its floating point approximation. " }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 58 "This work sheet, as well as the subsequent ones, are fully " }{TEXT 308 11 "inte ractive" }{TEXT -1 253 ". You can change each of the commands or parts of them, press \"Enter\" and see the results. Try changing numbers \+ and the location of parentheses in the example above. After you click \+ \"Enter\" on a command line the cursor jumps to the next command line. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 91 "Press \"Enter \" on the lines below. Do you expect to obtain the same output for bot h of them?" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 18 "3*5+2/7; evalf(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "(3*5+2)/7; evalf(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 87 "The portions \+ of a worksheet consisting of text or a series of command lines are cal led " }{TEXT 309 16 "execution groups" }{TEXT -1 77 ". To open a new e xecution group after what you have just typed simply press \"" }{TEXT 310 2 "[>" }{TEXT -1 228 "\" on the toolbar. To insert a new execution group before a portion of already typed text, if you ever need it, pl ace the cursor at the beginning of the text, go the \"Insert\" menu cl ick on \"Execution Group\", then \"Before Cursor\"." }}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 311 0 "" }{TEXT 256 5 "Note:" }{TEXT 312 1 " " }{TEXT 333 66 "If you want to interact successfully w ith a worksheet, you have to" }{TEXT 334 1 " " }{TEXT 318 10 "re-execu te" }{TEXT 319 1 " " }{TEXT 335 118 ", in sequence, all the commands i n it. That is, you have to click \"Enter\" on all commands lines, beg inning with the \"" }{TEXT 331 7 "restart" }{TEXT 332 571 "\" command, which clears Maple's internal memory of all prior assignments and def initions, forward. Even if command outputs were saved before, and the y appear already on screen, you still have to re-execute commands. It \+ may not matter with simple commands like the ones that you have seen a bove, but it does matter if a command defines or labels a function or \+ any other object. If you don't re-execute such commands you may see st range error messages as Maple will not recognize functions, expression s and other objects that have been defined in the worksheet you opened ." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 317 1 " " }}{PARA 4 "" 0 "" {TEXT -1 18 "Defining Functions " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 273 " As \+ you probably know calculus is a study of functions. In this section we show the proper syntax for defining and working with functions in Map le. The best way of learning syntax and illustrating what Maple can do is by examples. Hence we start from the following problem." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 256 10 "Example 1." }{TEXT 268 1 " " }{TEXT -1 97 " A rumor is spreading amon g a group of 200 people in an isolated region. The number of people, N (" }{TEXT 313 1 "t" }{TEXT -1 36 "), who have heard the rumor by time \+ " }{TEXT 267 1 "t" }{TEXT -1 1 "," }{TEXT 290 1 " " }{TEXT -1 8 "measu red" }{TEXT 266 0 "" }{TEXT 259 1 " " }{TEXT -1 90 "in hours since the rumor started to spread, can be approximated by the following functio n " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 257 "" 0 "" {XPPEDIT 18 0 "N(t) = 1.00503/(.503e-2+.84^t);" "6#/-%\"NG6#%\"tG*&-%&FloatG6$\"'.05 !\"&\"\"\",&-F*6$\"$.&F-F.)-F*6$\"#%)!\"#F'F.!\"\"" }{TEXT -1 4 " . " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 226 "How \+ many people have heard the rumor after 20 hours? After 30 hours? How l ong will it take for half of the population to have heard the rumor? W hen will practically everyone hear the rumor? When is the rumor spread ing fastest?" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 87 "Maple can answer all these questions for us. The first step is \+ defining the function N(" }{TEXT 270 1 "t" }{TEXT -1 54 ") in Maple. A function is defined in the following way" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "N:=t->1.00503/(.0050 3+.84^t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"NGf*6#%\"tG6\"6$%)ope ratorG%&arrowGF(,$*&\"\"\"F.,&$\"$.&!\"&F.)$\"#%)!\"#9$F.!\"\"$\"'.05F 2F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 48 "Note the \+ proper syntax for entering functions! \"" }{TEXT 314 1 "N" }{TEXT -1 32 "\" is the name of the function, \"" }{TEXT 315 2 ":=" }{TEXT -1 192 "\" means in Maple \"define\". As you know, a function is a rule w hich to each input, say t, prescribes the output given by the formula \+ for the function. The proper Maple syntax, using the arrow \"" }{TEXT 316 2 "->" }{TEXT -1 176 "\", reflects this interpretation of a functi on. You type the arrow using the \"minus\" and the \"greater\" keys. \+ Like every command in Maple, our definition ends with a semicolon. " } }{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 100 "The num ber of people who have heard the rumor after 20 hours is given by N(20 ). Once the function N(" }{TEXT 260 1 "t" }{TEXT -1 70 ") is defined, \+ we ask Maple to calculate N(20) using the simple syntax:" }}{PARA 0 " " 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "N(20) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+3!)\\@G!\")" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 92 "About 28 people have heard the rumor after 20 h ours. Let's calculate a few more values of N(" }{TEXT 271 1 "t" } {TEXT -1 2 ")." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 41 "N(0);N(30);N(35);N(40);N(50);N(60);N(70);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+++++5!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+u\\3#o*!\")" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+ %[)*GQ\"!\"(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+x&fYo\"!\"(" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+!H1^$>!\"(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+w[w')>!\"(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+R Z3'*>!\"(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 25 "As we see, initially, at " }{TEXT 281 4 " t = " }{TEXT -1 126 "0, only one person knows the rumor, then the numb er increases. After about 70 hours practically everybody has heard the rumor." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 282 6 "Note: " }{TEXT -1 13 "If you enter " }}{PARA 0 "" 0 " " {TEXT 280 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "M:=1.005 3/(.00503+.84^t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"MG,$*&\"\"\"F ',&$\"$.&!\"&F')$\"#%)!\"#%\"tGF'!\"\"$\"&`+\"!\"%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 23 "you have not defined a " }{TEXT 320 9 "function " }{TEXT -1 3 "of " } {TEXT 283 1 "t" }{TEXT -1 8 " but an " }{TEXT 321 10 "expression" } {TEXT -1 15 " M in terms of " }{TEXT 284 1 "t" }{TEXT -1 89 " . Maple \+ can process functions as well as expressions but the syntax is often d ifferent. " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT -1 8 "Plotting" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 " " {TEXT -1 93 "The best way to see how a given function behaves is by \+ ploting it. Let's plot the function N(" }{TEXT 275 1 "t" }{TEXT -1 82 ") of the above example. Clearly, the usefulness of our plot depends o n the proper " }{TEXT 322 19 "choice of the range" }{TEXT -1 168 " for our graph. The numbers above give us a pretty good idea that within a bout 70 hours practically everybody has heard the rumor. Hence, we sha ll graph the function N(" }{TEXT 272 1 "t" }{TEXT -1 6 ") for " } {TEXT 273 2 "t " }{TEXT -1 68 "between 0 and, say 75. The proper comma nd for graphing a function is" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "plot(N(t),t=0..75);" }} {PARA 13 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 261 "The graph shows clearly how the number of people who have heard the rumor increases, first sl owly as the graph climbs slowly, then faster, until it eventually leve ls off at about 200 when everyone knows the rumor. The rumor seems to \+ be spreading fastest around " }{TEXT 274 1 "t" }{TEXT -1 145 " = 30 as the curve seems steepest there. We shall be able to answer the questi on exactly later on in the course when we already know derivatives." } }{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 183 "We shal l make extensive use of Maple's plotting facility. You can plot functi ons without necessarily giving them names and defining them as in the \+ example above. You simply type the \"" }{TEXT 323 4 "plot" }{TEXT -1 169 "\" command and enter a formula for a function and the range you w ant it plotted in. Before clicking \"Enter\" on the lines below, try \+ to predict what you are going to see." }}{PARA 0 "" 0 "" {TEXT -1 0 " " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "plot(x^2,x=-2..2);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "plot(2*x^3,x=-1..3);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "plot(3*t+1,t=0..5);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT -1 17 "Solving Equations" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 177 "To answe r the remaining question of Example 1 \"When has half of the populatio n heard the rumor?\" we can try to estimate the time from the graph. I t seems that somewhere between " }{TEXT 278 1 "t" }{TEXT -1 9 " =30 an d " }{TEXT 279 1 "t" }{TEXT -1 89 " =35, 100 people have heard the rum or. To find that time precisely, we need to solve for " }{TEXT 291 1 " t" }{TEXT -1 16 " the equation N(" }{TEXT 276 1 "t" }{TEXT -1 7 ") = 1 00" }{TEXT 277 2 ". " }{TEXT -1 43 "Maple can solve equations and the \+ syntax is" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 18 "solve(N(t)=100,t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+IV^OI!\")" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 66 "After approximately 30.37 hours, 1 00 people have heard the rumor. " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT -1 314 "As you know, solving equations is no eas y matter. Maple's equation solver knows all standard methods for solvi ng equations, but for many equations there are no general methods for \+ solving them. In that case we shall resort to finding approximate solu tions by solving equations numerically, which is evoked by the \"" } {TEXT 324 6 "fsolve" }{TEXT -1 191 "\" command. We shall see examples \+ of that in subsequent worksheets. For reasonably simple equations Mapl e can find exact solutions even if a given equation contains letter co nstants, that is, " }{TEXT 325 10 "parameters" }{TEXT -1 13 ". For exa mple" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "solve(x^2+a*x+b=0,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$,&%\"aG#!\"\"\"\"#*$-%%sqrtG6#,&*$)F$F'\"\"\"F/%\"bG!\"%F/#F/F', &F$F%F(F%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT -1 16 "Using Map le Help" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 136 "Maple has an extensive on-line help and it may be a good idea to \+ learn how to use it. For example, you want to factor a polynomial, say " }}{PARA 262 "" 0 "" {XPPEDIT 18 0 "x^3-3*x-2;" "6#,(*$%\"xG\"\"$\" \"\"*&F&F'F%F'!\"\"\"\"#F)" }{TEXT -1 2 " ." }}{PARA 0 "" 0 "" {TEXT -1 597 "To find a Maple command to do this, select Topic Search... fro m the Help menu. Then type \"factor\" because that's what you want to \+ do. Among the choices that come up, you see \"Factor\" and \"factor\". Both look promising. Say you want to try \"Factor\" first. Click on i t to select it and then double click on it to open the corresponding H elp menu. A long page comes up. Scroll down to examples. The examples \+ look nothing like you want. Try \"factor\" instead. That's it! The fir st example on the page that comes up looks almost exactly as what you \+ want. It is an example of how to factor the polynomial " }{XPPEDIT 18 0 "6*x^2+18*x-24;" "6#,(*&\"\"'\"\"\"*$%\"xG\"\"#F&F&*&\"#=F&F(F&F&\"# C!\"\"" }{TEXT -1 346 ". You can remember the syntax and use it to so lve your example, or, if the syntax is complicated, you can copy an ex ample from Help menu into your worksheet as follows. Highlight the com mand line that you want to copy. Click on Copy under the Edit menu and close the Help screen. Open a new execution group in your worksheet b y clicking on the \"" }{TEXT 326 2 "[>" }{TEXT -1 38 "\" button. Move \+ the cursor to the new \"" }{TEXT 327 1 ">" }{TEXT -1 58 "\" prompt and then use Paste. Below we have done just that." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "factor(6*x^ 2+18*x-24);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 61 "Now we can simply \+ follow the syntax to factor our polynomial." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "factor(x^3-3*x-2) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&,&%\"xG\"\"\"!\"#F&F&),&F%F&F&F &\"\"#F&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 210 "Done. You could have arrived at the right help menu by typing \"polynomial\" instead of \" factor\", and navigating your way through a series of menus which appe ar on the top of the screen. Try this as an excercise." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT 292 17 "Homework Problems" }}{PARA 0 " " 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 320 "This, as well as \+ all subsequent Maple worksheets, contains homework problems. To solve \+ your homework problems open a new Maple worksheet by clicking on the b lank page icon on the toolbar. Enter your name, the title of the works heet to which the homework corresponds, numbers of consecutive problem s using the text mode \"" }{TEXT 336 1 "T" }{TEXT -1 82 "\". Usually, \+ all you need to solve homework problems is to read each worksheet and \+ " }{TEXT 328 9 "carefully" }{TEXT -1 108 " follow the syntax in it. Do not skip commas, semicolons, parentheses, stars denoting multiplicati on etc.. " }{TEXT 329 48 "Your syntax has to be precise in order to w ork. " }{TEXT -1 106 "After using Maple to plot graphs, perform calcul ations etc., whenever appropriate, as in Problem 1 below, " }{TEXT 337 40 "explain your answers in practical terms." }{TEXT -1 1 " " } {TEXT 330 81 "Your explanations, in complete sentences, should be type d using Maple's text mode" }{TEXT -1 4 ". " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 285 11 "Problem 1. " } {TEXT -1 17 "The population P(" }{TEXT 286 1 "t" }{TEXT -1 81 "), in t housands, of a town t years after January 1, 1990 is given by the func tion" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 258 "" 0 "" {XPPEDIT 18 0 "P(t) = 16.8+.3*t+.1*t^2;" "6#/-%\"PG6#%\"tG,(-%&FloatG6$\"$o\"!\"\" \"\"\"*&-F*6$\"\"$F-F.F'F.F.*&-F*6$F.F-F.*$F'\"\"#F.F." }{TEXT -1 2 " \+ ." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 27 "(a) \+ Define the function P(" }{TEXT 287 1 "t" }{TEXT -1 11 ") in Maple." } }{PARA 0 "" 0 "" {TEXT -1 67 "(b) What was the population on January 1 , 1996? On January 1, 1998?" }}{PARA 0 "" 0 "" {TEXT -1 80 "(c) Plot t he graph of the population from January 1, 1990 until January 1, 2010. " }}{PARA 0 "" 0 "" {TEXT -1 90 "(d) Assuming that the present trend c ontinues, when will the population reach 40 thousand?" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 288 11 "Proble m 2. " }{TEXT -1 40 "Find the exact and the decimal value for" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 259 "" 0 "" {XPPEDIT 18 0 "(30^( 1/4)+1)/(1+2^5)-(7+10)/8;" "6#,&*&,&)\"#I*&\"\"\"F)\"\"%!\"\"F)F)F)F), &F)F)*$\"\"#\"\"&F)F+F)*&,&\"\"(F)\"#5F)F)\"\")F+F+" }{TEXT -1 2 " ." }}{PARA 260 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" } {TEXT 289 12 "Problem 3. " }{TEXT -1 19 "Solve the equation " }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 261 "" 0 "" {XPPEDIT 18 0 "7+2*x -3*x^2 = 0;" "6#/,(\"\"(\"\"\"*&\"\"#F&%\"xGF&F&*&\"\"$F&*$F)F(F&!\"\" \"\"!" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 338 6 "Note. " }{TEXT 346 79 "When creating your homewo rk worksheets, you may choose to start them with the \"" }{TEXT 343 7 "restart" }{TEXT -1 1 "\"" }{TEXT 347 75 " command or you may not. Bot h ways have advantages and disadvantages. The \"" }{TEXT 339 7 "restar t" }{TEXT 348 301 "\" command clears Maple's memory from all prior def initions, assignments and starts Maple from scratch. This often helps \+ to avoid confusion. On the other hand, if in your homework problems yo u are asked to do more work with functions that were already defined i n the original worksheet and you use the " }{TEXT 340 8 "\"restart" } {TEXT 349 141 "\" command, you will have to redefine the functions as \+ the command erased them from Maple's memory. Follow your own judgement when using the \"" }{TEXT 341 7 "restart" }{TEXT 350 103 "\" command. For the homework in this worksheet, using or not using the command wi ll make no difference. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 " " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 23 "To understand how the \"" } {TEXT 342 7 "restart" }{TEXT -1 83 "\" command works, execute the comm and lines below, in sequence, at see what happens." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 36 "Maple has been started from scratch." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "f(2);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 69 "Maple doesn't know what f(2) is as no function f(x) has b een defined." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "f:=x->x^2;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 17 "The function \+ f , " }{XPPEDIT 18 0 "f(x) = x^2;" "6#/-%\"fG6#%\"xG*$F'\"\"#" }{TEXT -1 18 " has been defined." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "f(2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 27 "Maple knows t he function f." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "f(2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 30 "Again, Maple doesn't know f. " }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 344 77 "MTH 141 Maple Worksheets written by B. Ka skosz and L. Pakula, Copyright 1998." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 345 38 "Last modified August 1999. Update 2006" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}}{MARK "0 0 0" 8 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }